Kinds of infinity and the Book of Sand
The "Book of Sand" is one of the most accomplished Borge's stories about one of his favorite themes: how we, finite beings, can ever hope to grasp an actual infinity. The infinite quality of this book goes further than the intuitive notion that most persons have of the infinite: the counting numbers 1,2,3...
If you read the story carefully, you'll come across passages that imply the infinity of the book is "larger": despite being infinite, you can name, in principle, all the counting numbers and you can always find a particular one, however large, just by counting up to it; but the book in the story has an infinity of pages that cannot be named or, even if you come across it once, you'll never be able to find it again: it's a "higher" infinite (ok, for the mathematically inclined, the book's infinity is the one that associated with the real numbers, which is provably larger than the one associted with the counting numbers).
This story is probably the best non-mathematical description of this kind of infinity; the second best is, in my opinion, another one from Borges: The garden of forking paths.